Exploring and Explaining Complex Allometric Relationships:  A Case Study on Amniote Testes Mass Allometry

MacLeod, Colin D.

doi:10.3390/systems2030379

Cited by 7 publications

(9 citation statements)

References 24 publications

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“…Packard has considered deviations from linearity in log-log plots of allometry as mainly attributable to a logtransformation itself (Packard & Boardman, 2008;Packard, 2012a;Packard, 2012b;Packard, 2013). From this perspective, overcoming the bias due to curvature in log scale from this requires extending complexity of Huxley's model of simple allometry in direct scales which bears a paradigm of multiple parameter complex allometry (Gould, 1966;Lovett & Felder, 1989;MacLeod, 2014;Bervian et al 2006;Packard, 2012a).…”

Section: Discussionmentioning

confidence: 99%

“…It often occurs that even after contemplation of proper form for this TAMA's derived proxy for produces biased projections of observed values of the response . This means, that ( , ) complexity of Huxley's formula of simple allometry becomes inappropriate to identify ( , ) the true form (Gould, 1966;Huxley, 1932;Bervian et al 2006;MacLeod, 2014;( , ) Echavarria-Heras et al 2019). From the settings of equation 1it is reasonable assuming that adapting complexity as it is needed to identify could depend on MPCA forms.…”

Section: B2) Huxley's Formula Of Simple Allometrymentioning

confidence: 99%

“…From this standpoint, analysis must rely in Multiple Parameter Complex Allometry (MPCA after this) formalizations through all varieties of nonlinear or discontinuous relationships (e.g. Frankino et al 2010;MacLeod, 2014;Bervian et al 2006;Lovett & Felder, 1989;Packard 2013). But, adoption of MPCA Therefore, this structure naturally hosts heterogeneity as conceived by PLA.…”

Section: Introductionmentioning

confidence: 99%

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Peer Review #1 of "Assessment of a Takagi–Sugeno-Kang fuzzy model assembly for examination of polyphasic loglinear allometry (v0.1)"

Packard¹

2020

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Background. The traditional allometric analysis relies on log-transformation to contemplate linear regression in geometrical space then retransforming to get Huxley's model of simple allometry. Views assert this induces bias endorsing multi-parameter complex allometry forms and nonlinear regression in arithmetical scales. Defenders of traditional approach deem it necessary since generally organismal growth is essentially multiplicative. Then keeping allometry as originally envisioned by Huxley requires a paradigm of polyphasic loglinear allometry. A Takagi-Sugeno-Kang fuzzy model assembles a mixture of weighted sub models. This allows direct identification of break points for transition between phases. Then, this paradigm is seamlessly appropriate for efficient allometric examination of polyphasic loglinear allometry patterns. Here, we explore its suitability. Methods. Present fuzzy model embraces firing strength weights from Gaussian membership functions and linear consequents. Weights are identified by subtractive clustering and consequents through recursive least squares or maximum likelihood. Intersection of firing strength factors set criterion to estimate breakpoints. A multiparameter complex allometry model follows by adapting firing strengths by composite membership functions and linear consequents in arithmetical space. Results. Takagi-Sugeno-Kang surrogates adapted complexity depending on analyzed data set. Retransformation results conveyed reproducibility strength of similar proxies identified in arithmetical space. Breakpoints were straightforwardly identified. Retransformed form implies complex allometry as a generalization of Huxley's power model involving covariate depending parameters. Huxley reported a breakpoint in the log-log plot of chela mass vs body mass of fiddler crabs (Uca pugnax), attributed to a sudden change in relative growth of the chela approximately when crabs reach sexual maturity. G.C. Packard implied this breakpoint as putative. However, according to present fuzzy methods existence of a break point in Huxley's data could be validated. Conclusions. Offered scheme bears reliable

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Section: Discussionmentioning

confidence: 99%

Section: B2) Huxley's Formula Of Simple Allometrymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Peer Review #1 of "Assessment of a Takagi–Sugeno-Kang fuzzy model assembly for examination of polyphasic loglinear allometry (v0.1)"

Packard¹

2020

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“…From this standpoint, analysis must rely in Multiple Parameter Complex Allometry (MPCA after this) formalizations through all varieties of nonlinear or discontinuous relationships (e.g., Frankino, Emlen & Shingleton, 2010;MacLeod, 2014;Bervian, Fontoura & Haimovici, 2006;Lovett & Felder, 1989;Packard, 2013). However, adoption of MPCA approaches nourishes one of the most fundamental discrepancies among schools of allometric examination.…”

Section: Introductionmentioning

confidence: 99%

Assessment of a Takagi–Sugeno-Kang fuzzy model assembly for examination of polyphasic loglinear allometry

Echavarría-Heras

Castro-Rodríguez

Leal-Ramírez

et al. 2020

PeerJ

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Background The traditional allometric analysis relies on log- transformation to contemplate linear regression in geometrical space then retransforming to get Huxley’s model of simple allometry. Views assert this induces bias endorsing multi-parameter complex allometry forms and nonlinear regression in arithmetical scales. Defenders of traditional approach deem it necessary since generally organismal growth is essentially multiplicative. Then keeping allometry as originally envisioned by Huxley requires a paradigm of polyphasic loglinear allometry. A Takagi-Sugeno-Kang fuzzy model assembles a mixture of weighted sub models. This allows direct identification of break points for transition between phases. Then, this paradigm is seamlessly appropriate for efficient allometric examination of polyphasic loglinear allometry patterns. Here, we explore its suitability. Methods Present fuzzy model embraces firing strength weights from Gaussian membership functions and linear consequents. Weights are identified by subtractive clustering and consequents through recursive least squares or maximum likelihood. Intersection of firing strength factors set criterion to estimate breakpoints. A multi-parameter complex allometry model follows by adapting firing strengths by composite membership functions and linear consequents in arithmetical space. Results Takagi-Sugeno-Kang surrogates adapted complexity depending on analyzed data set. Retransformation results conveyed reproducibility strength of similar proxies identified in arithmetical space. Breakpoints were straightforwardly identified. Retransformed form implies complex allometry as a generalization of Huxley’s power model involving covariate depending parameters. Huxley reported a breakpoint in the log–log plot of chela mass vs. body mass of fiddler crabs (Uca pugnax), attributed to a sudden change in relative growth of the chela approximately when crabs reach sexual maturity. G.C. Packard implied this breakpoint as putative. However, according to present fuzzy methods existence of a break point in Huxley’s data could be validated. Conclusions Offered scheme bears reliable analysis of zero intercept allometries based on geometrical space protocols. Endorsed affine structure accommodates either polyphasic or simple allometry if whatever turns required. Interpretation of break points characterizing heterogeneity is intuitive. Analysis can be achieved in an interactive way. This could not have been obtained by relying on customary approaches. Besides, identification of break points in arithmetical scale is straightforward. Present Takagi-Sugeno-Kang arrangement offers a way to overcome the controversy between a school considering a log-transformation necessary and their critics claiming that consistent results can be only obtained through complex allometry models fitted by direct nonlinear regression in the original scales.

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“…Alongside this it is necessary to consider of multiple-parameter complex allometry (MCA). Related formulations can admit all sorts of nonlinear or discontinuous relationships intended to be fitted in arithmetical scales by means of DNLR protocols [75][76][77][78].…”

Section: Introductionmentioning

confidence: 99%

A Generalized Model of Complex Allometry I: Formal Setup, Identification Procedures and Applications to Non-Destructive Estimation of Plant Biomass Units

Echavarría-Heras¹,

Leal-Ramírez²,

Villa-Diharce³

et al. 2019

Applied Sciences

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(1) Background: We previously demonstrated that customary regression protocols for curvature in geometrical space all derive from a generalized model of complex allometry combining scaling parameters expressing as continuous functions of covariate. Results highlighted the relevance of addressing suitable complexity in enhancing the accuracy of allometric surrogates of plant biomass units. Nevertheless, examination was circumscribed to particular characterizations of the generalized model. Here we address the general identification problem. (2) Methods: We first suggest a log-scales protocol composing a mixture of linear models weighted by exponential powers. Alternatively, adopting an operating regime-based modeling slant we offer mixture regression or Takagi–Sugeno–Kang arrangements. This last approach allows polyphasic identification in direct scales. A derived index measures the extent on what complexity in arithmetic space drives curvature in arithmetical space. (3) Results: Fits on real and simulated data produced proxies of outstanding reproducibility strength indistinctly of data scales. (4) Conclusions: Presented analytical constructs are expected to grant efficient allometric projection of plant biomass units and also for the general settings of allometric examination. A traditional perspective deems log-transformation and allometry inseparable. Recent views assert that this leads to biased results. The present examination suggests this controversy can be resolved by addressing adequately the complexity of geometrical space protocols

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Exploring and Explaining Complex Allometric Relationships: A Case Study on Amniote Testes Mass Allometry

Cited by 7 publications

References 24 publications

Peer Review #1 of "Assessment of a Takagi–Sugeno-Kang fuzzy model assembly for examination of polyphasic loglinear allometry (v0.1)"

Peer Review #1 of "Assessment of a Takagi–Sugeno-Kang fuzzy model assembly for examination of polyphasic loglinear allometry (v0.1)"

Assessment of a Takagi–Sugeno-Kang fuzzy model assembly for examination of polyphasic loglinear allometry

A Generalized Model of Complex Allometry I: Formal Setup, Identification Procedures and Applications to Non-Destructive Estimation of Plant Biomass Units

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